Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(37,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-0.767178 - 1.18804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.109 |
Dual form | 144.2.k.c.37.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.767178 | − | 1.18804i | −0.542477 | − | 0.840071i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.822876 | + | 1.82288i | −0.411438 | + | 0.911438i | ||||
\(5\) | −2.37608 | + | 2.37608i | −1.06261 | + | 1.06261i | −0.0647108 | + | 0.997904i | \(0.520612\pi\) |
−0.997904 | + | 0.0647108i | \(0.979388\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.64575i | 1.37796i | 0.724778 | + | 0.688982i | \(0.241942\pi\) | ||||
−0.724778 | + | 0.688982i | \(0.758058\pi\) | |||||||
\(8\) | 2.79694 | − | 0.420861i | 0.988868 | − | 0.148797i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.64575 | + | 1.00000i | 1.46912 | + | 0.316228i | ||||
\(11\) | −0.841723 | + | 0.841723i | −0.253789 | + | 0.253789i | −0.822522 | − | 0.568733i | \(-0.807434\pi\) |
0.568733 | + | 0.822522i | \(0.307434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.64575 | − | 2.64575i | −0.733799 | − | 0.733799i | 0.237571 | − | 0.971370i | \(-0.423649\pi\) |
−0.971370 | + | 0.237571i | \(0.923649\pi\) | |||||||
\(14\) | 4.33130 | − | 2.79694i | 1.15759 | − | 0.747514i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.64575 | − | 3.00000i | −0.661438 | − | 0.750000i | ||||
\(17\) | 3.06871 | 0.744272 | 0.372136 | − | 0.928178i | \(-0.378625\pi\) | ||||
0.372136 | + | 0.928178i | \(0.378625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.64575 | + | 1.64575i | 0.377561 | + | 0.377561i | 0.870222 | − | 0.492660i | \(-0.163976\pi\) |
−0.492660 | + | 0.870222i | \(0.663976\pi\) | |||||||
\(20\) | −2.37608 | − | 6.28651i | −0.531307 | − | 1.40571i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.64575 | + | 0.354249i | 0.350875 | + | 0.0755261i | ||||
\(23\) | 7.82087i | 1.63076i | 0.578923 | + | 0.815382i | \(0.303473\pi\) | ||||
−0.578923 | + | 0.815382i | \(0.696527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 6.29150i | − | 1.25830i | ||||||
\(26\) | −1.11349 | + | 5.17302i | −0.218374 | + | 1.01451i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.64575 | − | 3.00000i | −1.25593 | − | 0.566947i | ||||
\(29\) | −0.692633 | − | 0.692633i | −0.128619 | − | 0.128619i | 0.639867 | − | 0.768486i | \(-0.278989\pi\) |
−0.768486 | + | 0.639867i | \(0.778989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.354249 | −0.0636249 | −0.0318125 | − | 0.999494i | \(-0.510128\pi\) | ||||
−0.0318125 | + | 0.999494i | \(0.510128\pi\) | |||||||
\(32\) | −1.53436 | + | 5.44479i | −0.271238 | + | 0.962512i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.35425 | − | 3.64575i | −0.403750 | − | 0.625241i | ||||
\(35\) | −8.66259 | − | 8.66259i | −1.46425 | − | 1.46425i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.64575 | − | 4.64575i | 0.763757 | − | 0.763757i | −0.213242 | − | 0.976999i | \(-0.568402\pi\) |
0.976999 | + | 0.213242i | \(0.0684024\pi\) | |||||||
\(38\) | 0.692633 | − | 3.21780i | 0.112360 | − | 0.521996i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.64575 | + | 7.64575i | −0.892672 | + | 1.20890i | ||||
\(41\) | − | 6.43560i | − | 1.00507i | −0.864556 | − | 0.502536i | \(-0.832400\pi\) | ||
0.864556 | − | 0.502536i | \(-0.167600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.64575 | + | 5.64575i | −0.860969 | + | 0.860969i | −0.991451 | − | 0.130482i | \(-0.958348\pi\) |
0.130482 | + | 0.991451i | \(0.458348\pi\) | |||||||
\(44\) | −0.841723 | − | 2.22699i | −0.126894 | − | 0.335731i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.29150 | − | 6.00000i | 1.36996 | − | 0.884652i | ||||
\(47\) | 11.1878 | 1.63190 | 0.815951 | − | 0.578121i | \(-0.196214\pi\) | ||||
0.815951 | + | 0.578121i | \(0.196214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.29150 | −0.898786 | ||||||||
\(50\) | −7.47455 | + | 4.82670i | −1.05706 | + | 0.682599i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.00000 | − | 2.64575i | 0.970725 | − | 0.366900i | ||||
\(53\) | −5.44479 | + | 5.44479i | −0.747900 | + | 0.747900i | −0.974084 | − | 0.226185i | \(-0.927375\pi\) |
0.226185 | + | 0.974084i | \(0.427375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 1.53436 | + | 10.1969i | 0.205037 | + | 1.36262i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.291503 | + | 1.35425i | −0.0382762 | + | 0.177822i | ||||
\(59\) | 7.82087 | − | 7.82087i | 1.01819 | − | 1.01819i | 0.0183591 | − | 0.999831i | \(-0.494156\pi\) |
0.999831 | − | 0.0183591i | \(-0.00584422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.64575 | + | 4.64575i | 0.594828 | + | 0.594828i | 0.938932 | − | 0.344104i | \(-0.111817\pi\) |
−0.344104 | + | 0.938932i | \(0.611817\pi\) | |||||||
\(62\) | 0.271772 | + | 0.420861i | 0.0345151 | + | 0.0534495i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.64575 | − | 2.35425i | 0.955719 | − | 0.294281i | ||||
\(65\) | 12.5730 | 1.55949 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | + | 4.00000i | 0.488678 | + | 0.488678i | 0.907889 | − | 0.419211i | \(-0.137693\pi\) |
−0.419211 | + | 0.907889i | \(0.637693\pi\) | |||||||
\(68\) | −2.52517 | + | 5.59388i | −0.306222 | + | 0.678358i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.64575 | + | 16.9373i | −0.435751 | + | 2.02439i | ||||
\(71\) | − | 3.36689i | − | 0.399577i | −0.979839 | − | 0.199788i | \(-0.935975\pi\) | ||
0.979839 | − | 0.199788i | \(-0.0640254\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.29150i | 0.853406i | 0.904392 | + | 0.426703i | \(0.140325\pi\) | ||||
−0.904392 | + | 0.426703i | \(0.859675\pi\) | |||||||
\(74\) | −9.08345 | − | 1.95522i | −1.05593 | − | 0.227289i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.35425 | + | 1.64575i | −0.499467 | + | 0.188781i | ||||
\(77\) | −3.06871 | − | 3.06871i | −0.349712 | − | 0.349712i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.35425 | 0.489891 | 0.244946 | − | 0.969537i | \(-0.421230\pi\) | ||||
0.244946 | + | 0.969537i | \(0.421230\pi\) | |||||||
\(80\) | 13.4148 | + | 0.841723i | 1.49981 | + | 0.0941075i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.64575 | + | 4.93725i | −0.844332 | + | 0.545228i | ||||
\(83\) | 0.841723 | + | 0.841723i | 0.0923911 | + | 0.0923911i | 0.751792 | − | 0.659401i | \(-0.229190\pi\) |
−0.659401 | + | 0.751792i | \(0.729190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.29150 | + | 7.29150i | −0.790875 | + | 0.790875i | ||||
\(86\) | 11.0387 | + | 2.37608i | 1.19033 | + | 0.256219i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | + | 2.70850i | −0.213201 | + | 0.288727i | ||||
\(89\) | − | 9.50432i | − | 1.00746i | −0.863862 | − | 0.503728i | \(-0.831961\pi\) | ||
0.863862 | − | 0.503728i | \(-0.168039\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.64575 | − | 9.64575i | 1.01115 | − | 1.01115i | ||||
\(92\) | −14.2565 | − | 6.43560i | −1.48634 | − | 0.670958i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.58301 | − | 13.2915i | −0.885269 | − | 1.37091i | ||||
\(95\) | −7.82087 | −0.802404 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5830 | 1.07454 | 0.537271 | − | 0.843410i | \(-0.319455\pi\) | ||||
0.537271 | + | 0.843410i | \(0.319455\pi\) | |||||||
\(98\) | 4.82670 | + | 7.47455i | 0.487571 | + | 0.755044i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.4686 | + | 5.17712i | 1.14686 | + | 0.517712i | ||||
\(101\) | −2.37608 | + | 2.37608i | −0.236429 | + | 0.236429i | −0.815370 | − | 0.578941i | \(-0.803466\pi\) |
0.578941 | + | 0.815370i | \(0.303466\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.06275i | 0.104715i | 0.998628 | + | 0.0523577i | \(0.0166736\pi\) | ||||
−0.998628 | + | 0.0523577i | \(0.983326\pi\) | |||||||
\(104\) | −8.51350 | − | 6.28651i | −0.834818 | − | 0.616443i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6458 | + | 2.29150i | 1.03401 | + | 0.222570i | ||||
\(107\) | −9.50432 | + | 9.50432i | −0.918817 | + | 0.918817i | −0.996943 | − | 0.0781266i | \(-0.975106\pi\) |
0.0781266 | + | 0.996943i | \(0.475106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.35425 | − | 1.35425i | −0.129713 | − | 0.129713i | 0.639269 | − | 0.768983i | \(-0.279237\pi\) |
−0.768983 | + | 0.639269i | \(0.779237\pi\) | |||||||
\(110\) | −4.75216 | + | 3.06871i | −0.453100 | + | 0.292590i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.9373 | − | 9.64575i | 1.03347 | − | 0.911438i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.5830 | − | 18.5830i | −1.73287 | − | 1.73287i | ||||
\(116\) | 1.83254 | − | 0.692633i | 0.170147 | − | 0.0643094i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.2915 | − | 3.29150i | −1.40770 | − | 0.303007i | ||||
\(119\) | 11.1878i | 1.02558i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.58301i | 0.871182i | ||||||||
\(122\) | 1.95522 | − | 9.08345i | 0.177017 | − | 0.822377i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.291503 | − | 0.645751i | 0.0261777 | − | 0.0579902i | ||||
\(125\) | 3.06871 | + | 3.06871i | 0.274474 | + | 0.274474i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.9373 | −1.32547 | −0.662733 | − | 0.748855i | \(-0.730604\pi\) | ||||
−0.662733 | + | 0.748855i | \(0.730604\pi\) | |||||||
\(128\) | −8.66259 | − | 7.27733i | −0.765672 | − | 0.643231i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.64575 | − | 14.9373i | −0.845988 | − | 1.31008i | ||||
\(131\) | −1.68345 | − | 1.68345i | −0.147083 | − | 0.147083i | 0.629730 | − | 0.776814i | \(-0.283165\pi\) |
−0.776814 | + | 0.629730i | \(0.783165\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | 1.68345 | − | 7.82087i | 0.145428 | − | 0.675620i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.58301 | − | 1.29150i | 0.735987 | − | 0.110745i | ||||
\(137\) | 15.9399i | 1.36184i | 0.732358 | + | 0.680920i | \(0.238420\pi\) | ||||
−0.732358 | + | 0.680920i | \(0.761580\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.58301 | − | 6.58301i | 0.558363 | − | 0.558363i | −0.370478 | − | 0.928841i | \(-0.620806\pi\) |
0.928841 | + | 0.370478i | \(0.120806\pi\) | |||||||
\(140\) | 22.9191 | − | 8.66259i | 1.93701 | − | 0.732123i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | + | 2.58301i | −0.335673 | + | 0.216761i | ||||
\(143\) | 4.45398 | 0.372460 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.29150 | 0.273344 | ||||||||
\(146\) | 8.66259 | − | 5.59388i | 0.716921 | − | 0.462953i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.64575 | + | 12.2915i | 0.381878 | + | 1.01036i | ||||
\(149\) | 3.76135 | − | 3.76135i | 0.308141 | − | 0.308141i | −0.536047 | − | 0.844188i | \(-0.680083\pi\) |
0.844188 | + | 0.536047i | \(0.180083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.6458i | − | 1.27323i | −0.771180 | − | 0.636617i | \(-0.780333\pi\) | ||
0.771180 | − | 0.636617i | \(-0.219667\pi\) | |||||||
\(152\) | 5.29570 | + | 3.91044i | 0.429538 | + | 0.317178i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.29150 | + | 6.00000i | −0.104072 | + | 0.483494i | ||||
\(155\) | 0.841723 | − | 0.841723i | 0.0676088 | − | 0.0676088i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.35425 | − | 1.35425i | −0.108081 | − | 0.108081i | 0.650998 | − | 0.759079i | \(-0.274350\pi\) |
−0.759079 | + | 0.650998i | \(0.774350\pi\) | |||||||
\(158\) | −3.34048 | − | 5.17302i | −0.265755 | − | 0.411543i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.29150 | − | 16.5830i | −0.734558 | − | 1.31100i | ||||
\(161\) | −28.5129 | −2.24714 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.35425 | + | 6.35425i | 0.497703 | + | 0.497703i | 0.910722 | − | 0.413019i | \(-0.135526\pi\) |
−0.413019 | + | 0.910722i | \(0.635526\pi\) | |||||||
\(164\) | 11.7313 | + | 5.29570i | 0.916061 | + | 0.413525i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.354249 | − | 1.64575i | 0.0274950 | − | 0.127735i | ||||
\(167\) | − | 4.45398i | − | 0.344659i | −0.985039 | − | 0.172330i | \(-0.944871\pi\) | ||
0.985039 | − | 0.172330i | \(-0.0551294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000i | 0.0769231i | ||||||||
\(170\) | 14.2565 | + | 3.06871i | 1.09342 | + | 0.235359i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.64575 | − | 14.9373i | −0.430485 | − | 1.13895i | ||||
\(173\) | 5.44479 | + | 5.44479i | 0.413960 | + | 0.413960i | 0.883115 | − | 0.469156i | \(-0.155442\pi\) |
−0.469156 | + | 0.883115i | \(0.655442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.9373 | 1.73389 | ||||||||
\(176\) | 4.75216 | + | 0.298179i | 0.358207 | + | 0.0224761i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.2915 | + | 7.29150i | −0.846334 | + | 0.546521i | ||||
\(179\) | 9.50432 | + | 9.50432i | 0.710386 | + | 0.710386i | 0.966616 | − | 0.256230i | \(-0.0824804\pi\) |
−0.256230 | + | 0.966616i | \(0.582480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.64575 | − | 4.64575i | 0.345316 | − | 0.345316i | −0.513045 | − | 0.858361i | \(-0.671483\pi\) |
0.858361 | + | 0.513045i | \(0.171483\pi\) | |||||||
\(182\) | −18.8595 | − | 4.05952i | −1.39796 | − | 0.300912i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.29150 | + | 21.8745i | 0.242653 | + | 1.61261i | ||||
\(185\) | 22.0773i | 1.62316i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.58301 | + | 2.58301i | −0.188888 | + | 0.188888i | ||||
\(188\) | −9.20614 | + | 20.3939i | −0.671427 | + | 1.48738i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | + | 9.29150i | 0.435286 | + | 0.674076i | ||||
\(191\) | −11.1878 | −0.809518 | −0.404759 | − | 0.914423i | \(-0.632645\pi\) | ||||
−0.404759 | + | 0.914423i | \(0.632645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.8745 | −1.43060 | −0.715299 | − | 0.698818i | \(-0.753710\pi\) | ||||
−0.715299 | + | 0.698818i | \(0.753710\pi\) | |||||||
\(194\) | −8.11905 | − | 12.5730i | −0.582914 | − | 0.902691i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.17712 | − | 11.4686i | 0.369795 | − | 0.819188i | ||||
\(197\) | 8.81168 | − | 8.81168i | 0.627806 | − | 0.627806i | −0.319709 | − | 0.947516i | \(-0.603585\pi\) |
0.947516 | + | 0.319709i | \(0.103585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.35425i | 0.592217i | 0.955154 | + | 0.296108i | \(0.0956890\pi\) | ||||
−0.955154 | + | 0.296108i | \(0.904311\pi\) | |||||||
\(200\) | −2.64785 | − | 17.5970i | −0.187231 | − | 1.24429i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.64575 | + | 1.00000i | 0.326874 | + | 0.0703598i | ||||
\(203\) | 2.52517 | − | 2.52517i | 0.177232 | − | 0.177232i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.2915 | + | 15.2915i | 1.06800 | + | 1.06800i | ||||
\(206\) | 1.26258 | − | 0.815315i | 0.0879684 | − | 0.0568057i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.937254 | + | 14.9373i | −0.0649869 | + | 1.03571i | ||||
\(209\) | −2.77053 | −0.191642 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.58301 | + | 6.58301i | 0.453193 | + | 0.453193i | 0.896413 | − | 0.443220i | \(-0.146164\pi\) |
−0.443220 | + | 0.896413i | \(0.646164\pi\) | |||||||
\(212\) | −5.44479 | − | 14.4056i | −0.373950 | − | 0.989378i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.5830 | + | 4.00000i | 1.27031 | + | 0.273434i | ||||
\(215\) | − | 26.8295i | − | 1.82976i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.29150i | − | 0.0876729i | ||||||
\(218\) | −0.569951 | + | 2.64785i | −0.0386020 | + | 0.179335i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.29150 | + | 3.29150i | 0.491593 | + | 0.221913i | ||||
\(221\) | −8.11905 | − | 8.11905i | −0.546146 | − | 0.546146i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.6458 | −1.31558 | −0.657788 | − | 0.753203i | \(-0.728508\pi\) | ||||
−0.657788 | + | 0.753203i | \(0.728508\pi\) | |||||||
\(224\) | −19.8504 | − | 5.59388i | −1.32631 | − | 0.373757i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.1669 | + | 18.1669i | 1.20578 | + | 1.20578i | 0.972381 | + | 0.233399i | \(0.0749848\pi\) |
0.233399 | + | 0.972381i | \(0.425015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.06275 | − | 2.06275i | 0.136310 | − | 0.136310i | −0.635659 | − | 0.771970i | \(-0.719272\pi\) |
0.771970 | + | 0.635659i | \(0.219272\pi\) | |||||||
\(230\) | −7.82087 | + | 36.3338i | −0.515693 | + | 2.39578i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.22876 | − | 1.64575i | −0.146325 | − | 0.108049i | ||||
\(233\) | − | 21.7792i | − | 1.42680i | −0.700757 | − | 0.713400i | \(-0.747154\pi\) | ||
0.700757 | − | 0.713400i | \(-0.252846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.5830 | + | 26.5830i | −1.73408 | + | 1.73408i | ||||
\(236\) | 7.82087 | + | 20.6921i | 0.509095 | + | 1.34694i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.2915 | − | 8.58301i | 0.861560 | − | 0.556354i | ||||
\(239\) | −23.4626 | −1.51767 | −0.758835 | − | 0.651283i | \(-0.774231\pi\) | ||||
−0.758835 | + | 0.651283i | \(0.774231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.29150 | 0.598518 | 0.299259 | − | 0.954172i | \(-0.403260\pi\) | ||||
0.299259 | + | 0.954172i | \(0.403260\pi\) | |||||||
\(242\) | 11.3850 | − | 7.35187i | 0.731855 | − | 0.472596i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.2915 | + | 4.64575i | −0.786883 | + | 0.297414i | ||||
\(245\) | 14.9491 | − | 14.9491i | 0.955063 | − | 0.955063i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.70850i | − | 0.554108i | ||||||
\(248\) | −0.990812 | + | 0.149090i | −0.0629167 | + | 0.00946720i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.29150 | − | 6.00000i | 0.0816818 | − | 0.379473i | ||||
\(251\) | −13.1166 | + | 13.1166i | −0.827911 | + | 0.827911i | −0.987228 | − | 0.159317i | \(-0.949071\pi\) |
0.159317 | + | 0.987228i | \(0.449071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.58301 | − | 6.58301i | −0.413870 | − | 0.413870i | ||||
\(254\) | 11.4595 | + | 17.7460i | 0.719035 | + | 1.11349i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.00000 | + | 15.8745i | −0.125000 | + | 0.992157i | ||||
\(257\) | 16.2381 | 1.01290 | 0.506452 | − | 0.862268i | \(-0.330957\pi\) | ||||
0.506452 | + | 0.862268i | \(0.330957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.9373 | + | 16.9373i | 1.05243 | + | 1.05243i | ||||
\(260\) | −10.3460 | + | 22.9191i | −0.641634 | + | 1.42138i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.708497 | + | 3.29150i | −0.0437711 | + | 0.203350i | ||||
\(263\) | − | 15.6417i | − | 0.964511i | −0.876031 | − | 0.482256i | \(-0.839818\pi\) | ||
0.876031 | − | 0.482256i | \(-0.160182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 25.8745i | − | 1.58946i | ||||||
\(266\) | 11.7313 | + | 2.52517i | 0.719292 | + | 0.154828i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.5830 | + | 4.00000i | −0.646460 | + | 0.244339i | ||||
\(269\) | 8.51350 | + | 8.51350i | 0.519077 | + | 0.519077i | 0.917292 | − | 0.398215i | \(-0.130370\pi\) |
−0.398215 | + | 0.917292i | \(0.630370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6458 | 0.707429 | 0.353715 | − | 0.935353i | \(-0.384918\pi\) | ||||
0.353715 | + | 0.935353i | \(0.384918\pi\) | |||||||
\(272\) | −8.11905 | − | 9.20614i | −0.492290 | − | 0.558204i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.9373 | − | 12.2288i | 1.14404 | − | 0.738766i | ||||
\(275\) | 5.29570 | + | 5.29570i | 0.319343 | + | 0.319343i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.5203 | − | 20.5203i | 1.23294 | − | 1.23294i | 0.270115 | − | 0.962828i | \(-0.412938\pi\) |
0.962828 | − | 0.270115i | \(-0.0870616\pi\) | |||||||
\(278\) | −12.8712 | − | 2.77053i | −0.771964 | − | 0.166166i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −27.8745 | − | 20.5830i | −1.66582 | − | 1.23007i | ||||
\(281\) | − | 9.50432i | − | 0.566980i | −0.958975 | − | 0.283490i | \(-0.908508\pi\) | ||
0.958975 | − | 0.283490i | \(-0.0914923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.5830 | − | 18.5830i | 1.10465 | − | 1.10465i | 0.110803 | − | 0.993842i | \(-0.464658\pi\) |
0.993842 | − | 0.110803i | \(-0.0353421\pi\) | |||||||
\(284\) | 6.13742 | + | 2.77053i | 0.364189 | + | 0.164401i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.41699 | − | 5.29150i | −0.202051 | − | 0.312893i | ||||
\(287\) | 23.4626 | 1.38495 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.58301 | −0.446059 | ||||||||
\(290\) | −2.52517 | − | 3.91044i | −0.148283 | − | 0.229629i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.2915 | − | 6.00000i | −0.777826 | − | 0.351123i | ||||
\(293\) | 14.9491 | − | 14.9491i | 0.873336 | − | 0.873336i | −0.119498 | − | 0.992834i | \(-0.538129\pi\) |
0.992834 | + | 0.119498i | \(0.0381286\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 37.1660i | 2.16389i | ||||||||
\(296\) | 11.0387 | − | 14.9491i | 0.641610 | − | 0.868899i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.35425 | − | 1.58301i | −0.426020 | − | 0.0917010i | ||||
\(299\) | 20.6921 | − | 20.6921i | 1.19665 | − | 1.19665i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.5830 | − | 20.5830i | −1.18638 | − | 1.18638i | ||||
\(302\) | −18.5878 | + | 12.0031i | −1.06961 | + | 0.690699i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.583005 | − | 9.29150i | 0.0334376 | − | 0.532904i | ||||
\(305\) | −22.0773 | −1.26415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | − | 20.0000i | −1.14146 | − | 1.14146i | −0.988183 | − | 0.153277i | \(-0.951017\pi\) |
−0.153277 | − | 0.988183i | \(-0.548983\pi\) | |||||||
\(308\) | 8.11905 | − | 3.06871i | 0.462626 | − | 0.174856i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.64575 | − | 0.354249i | −0.0934724 | − | 0.0201200i | ||||
\(311\) | − | 15.6417i | − | 0.886962i | −0.896284 | − | 0.443481i | \(-0.853743\pi\) | ||
0.896284 | − | 0.443481i | \(-0.146257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.29150i | − | 0.0730000i | −0.999334 | − | 0.0365000i | \(-0.988379\pi\) | ||
0.999334 | − | 0.0365000i | \(-0.0116209\pi\) | |||||||
\(314\) | −0.569951 | + | 2.64785i | −0.0321642 | + | 0.149427i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.58301 | + | 7.93725i | −0.201560 | + | 0.446505i | ||||
\(317\) | 2.37608 | + | 2.37608i | 0.133454 | + | 0.133454i | 0.770678 | − | 0.637224i | \(-0.219918\pi\) |
−0.637224 | + | 0.770678i | \(0.719918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.16601 | 0.0652841 | ||||||||
\(320\) | −12.5730 | + | 23.7608i | −0.702854 | + | 1.32827i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 21.8745 | + | 33.8745i | 1.21902 | + | 1.88775i | ||||
\(323\) | 5.05034 | + | 5.05034i | 0.281008 | + | 0.281008i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.6458 | + | 16.6458i | −0.923340 | + | 0.923340i | ||||
\(326\) | 2.67426 | − | 12.4239i | 0.148113 | − | 0.688098i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.70850 | − | 18.0000i | −0.149552 | − | 0.993884i | ||||
\(329\) | 40.7878i | 2.24870i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | + | 8.00000i | −0.439720 | + | 0.439720i | −0.891918 | − | 0.452198i | \(-0.850640\pi\) |
0.452198 | + | 0.891918i | \(0.350640\pi\) | |||||||
\(332\) | −2.22699 | + | 0.841723i | −0.122222 | + | 0.0461955i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.29150 | + | 3.41699i | −0.289538 | + | 0.186970i | ||||
\(335\) | −19.0086 | −1.03855 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.2915 | 0.832981 | 0.416491 | − | 0.909140i | \(-0.363260\pi\) | ||||
0.416491 | + | 0.909140i | \(0.363260\pi\) | |||||||
\(338\) | 1.18804 | − | 0.767178i | 0.0646208 | − | 0.0417290i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.29150 | − | 19.2915i | −0.395437 | − | 1.04623i | ||||
\(341\) | 0.298179 | − | 0.298179i | 0.0161473 | − | 0.0161473i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.58301i | 0.139469i | ||||||||
\(344\) | −13.4148 | + | 18.1669i | −0.723275 | + | 0.979494i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.29150 | − | 10.6458i | 0.123192 | − | 0.572319i | ||||
\(347\) | −0.841723 | + | 0.841723i | −0.0451861 | + | 0.0451861i | −0.729339 | − | 0.684153i | \(-0.760172\pi\) |
0.684153 | + | 0.729339i | \(0.260172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.2288 | − | 23.2288i | −1.24341 | − | 1.24341i | −0.958579 | − | 0.284828i | \(-0.908063\pi\) |
−0.284828 | − | 0.958579i | \(-0.591937\pi\) | |||||||
\(350\) | −17.5970 | − | 27.2504i | −0.940597 | − | 1.45659i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.29150 | − | 5.87451i | −0.175438 | − | 0.313112i | ||||
\(353\) | −28.5129 | −1.51759 | −0.758796 | − | 0.651329i | \(-0.774212\pi\) | ||||
−0.758796 | + | 0.651329i | \(0.774212\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | + | 8.00000i | 0.424596 | + | 0.424596i | ||||
\(356\) | 17.3252 | + | 7.82087i | 0.918233 | + | 0.414505i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00000 | − | 18.5830i | 0.211407 | − | 0.982142i | ||||
\(359\) | 19.0086i | 1.00324i | 0.865089 | + | 0.501619i | \(0.167262\pi\) | ||||
−0.865089 | + | 0.501619i | \(0.832738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 13.5830i | − | 0.714895i | ||||||
\(362\) | −9.08345 | − | 1.95522i | −0.477416 | − | 0.102764i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.64575 | + | 25.5203i | 0.505575 | + | 1.33763i | ||||
\(365\) | −17.3252 | − | 17.3252i | −0.906842 | − | 0.906842i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.8118 | −0.668769 | −0.334384 | − | 0.942437i | \(-0.608528\pi\) | ||||
−0.334384 | + | 0.942437i | \(0.608528\pi\) | |||||||
\(368\) | 23.4626 | − | 20.6921i | 1.22307 | − | 1.07865i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.2288 | − | 16.9373i | 1.36357 | − | 0.880526i | ||||
\(371\) | −19.8504 | − | 19.8504i | −1.03058 | − | 1.03058i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.93725 | + | 3.93725i | −0.203863 | + | 0.203863i | −0.801653 | − | 0.597790i | \(-0.796046\pi\) |
0.597790 | + | 0.801653i | \(0.296046\pi\) | |||||||
\(374\) | 5.05034 | + | 1.08709i | 0.261147 | + | 0.0562119i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.2915 | − | 4.70850i | 1.61374 | − | 0.242822i | ||||
\(377\) | 3.66507i | 0.188761i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6458 | − | 13.6458i | 0.700935 | − | 0.700935i | −0.263676 | − | 0.964611i | \(-0.584935\pi\) |
0.964611 | + | 0.263676i | \(0.0849350\pi\) | |||||||
\(380\) | 6.43560 | − | 14.2565i | 0.330140 | − | 0.731342i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.58301 | + | 13.2915i | 0.439145 | + | 0.680052i | ||||
\(383\) | 11.1878 | 0.571668 | 0.285834 | − | 0.958279i | \(-0.407729\pi\) | ||||
0.285834 | + | 0.958279i | \(0.407729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.5830 | 0.743219 | ||||||||
\(386\) | 15.2473 | + | 23.6117i | 0.776066 | + | 1.20180i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.70850 | + | 19.2915i | −0.442107 | + | 0.979378i | ||||
\(389\) | −7.42642 | + | 7.42642i | −0.376534 | + | 0.376534i | −0.869850 | − | 0.493316i | \(-0.835785\pi\) |
0.493316 | + | 0.869850i | \(0.335785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000i | 1.21373i | ||||||||
\(392\) | −17.5970 | + | 2.64785i | −0.888781 | + | 0.133737i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.2288 | − | 3.70850i | −0.867972 | − | 0.186831i | ||||
\(395\) | −10.3460 | + | 10.3460i | −0.520566 | + | 0.520566i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9373 | + | 23.9373i | 1.20138 | + | 1.20138i | 0.973748 | + | 0.227628i | \(0.0730971\pi\) |
0.227628 | + | 0.973748i | \(0.426903\pi\) | |||||||
\(398\) | 9.92518 | − | 6.40920i | 0.497504 | − | 0.321264i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.8745 | + | 16.6458i | −0.943725 | + | 0.832288i | ||||
\(401\) | 9.20614 | 0.459733 | 0.229866 | − | 0.973222i | \(-0.426171\pi\) | ||||
0.229866 | + | 0.973222i | \(0.426171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.937254 | + | 0.937254i | 0.0466879 | + | 0.0466879i | ||||
\(404\) | −2.37608 | − | 6.28651i | −0.118214 | − | 0.312766i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.93725 | − | 1.06275i | −0.245032 | − | 0.0527432i | ||||
\(407\) | 7.82087i | 0.387666i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.1660i | 0.848805i | 0.905474 | + | 0.424402i | \(0.139516\pi\) | ||||
−0.905474 | + | 0.424402i | \(0.860484\pi\) | |||||||
\(410\) | 6.43560 | − | 29.8982i | 0.317832 | − | 1.47657i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.93725 | − | 0.874508i | −0.0954417 | − | 0.0430839i | ||||
\(413\) | 28.5129 | + | 28.5129i | 1.40303 | + | 1.40303i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 18.4651 | − | 10.3460i | 0.905325 | − | 0.507256i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.12549 | + | 3.29150i | 0.103961 | + | 0.160993i | ||||
\(419\) | 13.1166 | + | 13.1166i | 0.640786 | + | 0.640786i | 0.950749 | − | 0.309962i | \(-0.100316\pi\) |
−0.309962 | + | 0.950749i | \(0.600316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6458 | − | 16.6458i | 0.811264 | − | 0.811264i | −0.173559 | − | 0.984823i | \(-0.555527\pi\) |
0.984823 | + | 0.173559i | \(0.0555268\pi\) | |||||||
\(422\) | 2.77053 | − | 12.8712i | 0.134867 | − | 0.626561i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.9373 | + | 17.5203i | −0.628289 | + | 0.850859i | ||||
\(425\) | − | 19.3068i | − | 0.936518i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.9373 | + | 16.9373i | −0.819651 | + | 0.819651i | ||||
\(428\) | −9.50432 | − | 25.1461i | −0.459408 | − | 1.21548i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −31.8745 | + | 20.5830i | −1.53713 | + | 0.992601i | ||||
\(431\) | 1.08709 | 0.0523632 | 0.0261816 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261816 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | −1.53436 | + | 0.990812i | −0.0736515 | + | 0.0475605i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.58301 | − | 1.35425i | 0.171595 | − | 0.0648567i | ||||
\(437\) | −12.8712 | + | 12.8712i | −0.615713 | + | 0.615713i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 37.5203i | − | 1.79074i | −0.445319 | − | 0.895372i | \(-0.646910\pi\) | ||
0.445319 | − | 0.895372i | \(-0.353090\pi\) | |||||||
\(440\) | −1.68345 | − | 11.1878i | −0.0802551 | − | 0.533356i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.41699 | + | 15.8745i | −0.162530 | + | 0.755073i | ||||
\(443\) | −23.2172 | + | 23.2172i | −1.10308 | + | 1.10308i | −0.109048 | + | 0.994036i | \(0.534780\pi\) |
−0.994036 | + | 0.109048i | \(0.965220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.5830 | + | 22.5830i | 1.07054 | + | 1.07054i | ||||
\(446\) | 15.0718 | + | 23.3399i | 0.713670 | + | 1.10518i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.58301 | + | 27.8745i | 0.405509 | + | 1.31695i | ||||
\(449\) | 37.7191 | 1.78007 | 0.890037 | − | 0.455889i | \(-0.150678\pi\) | ||||
0.890037 | + | 0.455889i | \(0.150678\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.41699 | + | 5.41699i | 0.255076 | + | 0.255076i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.64575 | − | 35.5203i | 0.358833 | − | 1.66705i | ||||
\(455\) | 45.8381i | 2.14892i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.5830i | 1.24350i | 0.783216 | + | 0.621750i | \(0.213578\pi\) | ||||
−0.783216 | + | 0.621750i | \(0.786422\pi\) | |||||||
\(458\) | −4.03312 | − | 0.868130i | −0.188455 | − | 0.0405651i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 49.1660 | − | 18.5830i | 2.29238 | − | 0.866437i | ||||
\(461\) | −8.81168 | − | 8.81168i | −0.410401 | − | 0.410401i | 0.471477 | − | 0.881878i | \(-0.343721\pi\) |
−0.881878 | + | 0.471477i | \(0.843721\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.9373 | 1.43778 | 0.718888 | − | 0.695126i | \(-0.244651\pi\) | ||||
0.718888 | + | 0.695126i | \(0.244651\pi\) | |||||||
\(464\) | −0.245364 | + | 3.91044i | −0.0113908 | + | 0.181537i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.8745 | + | 16.7085i | −1.19861 | + | 0.774006i | ||||
\(467\) | −11.4331 | − | 11.4331i | −0.529062 | − | 0.529062i | 0.391231 | − | 0.920293i | \(-0.372049\pi\) |
−0.920293 | + | 0.391231i | \(0.872049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.5830 | + | 14.5830i | −0.673381 | + | 0.673381i | ||||
\(470\) | 51.9756 | + | 11.1878i | 2.39745 | + | 0.516053i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.5830 | − | 25.1660i | 0.855352 | − | 1.15836i | ||||
\(473\) | − | 9.50432i | − | 0.437009i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3542 | − | 10.3542i | 0.475086 | − | 0.475086i | ||||
\(476\) | −20.3939 | − | 9.20614i | −0.934753 | − | 0.421963i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000 | + | 27.8745i | 0.823301 | + | 1.27495i | ||||
\(479\) | −12.2748 | −0.560852 | −0.280426 | − | 0.959876i | \(-0.590476\pi\) | ||||
−0.280426 | + | 0.959876i | \(0.590476\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.5830 | −1.12089 | ||||||||
\(482\) | −7.12824 | − | 11.0387i | −0.324682 | − | 0.502798i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.4686 | − | 7.88562i | −0.794028 | − | 0.358437i | ||||
\(485\) | −25.1461 | + | 25.1461i | −1.14182 | + | 1.14182i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18.2288i | − | 0.826024i | −0.910726 | − | 0.413012i | \(-0.864477\pi\) | ||
0.910726 | − | 0.413012i | \(-0.135523\pi\) | |||||||
\(488\) | 14.9491 | + | 11.0387i | 0.676714 | + | 0.499697i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −29.2288 | − | 6.29150i | −1.32042 | − | 0.284221i | ||||
\(491\) | 13.9583 | − | 13.9583i | 0.629929 | − | 0.629929i | −0.318121 | − | 0.948050i | \(-0.603052\pi\) |
0.948050 | + | 0.318121i | \(0.103052\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.12549 | − | 2.12549i | −0.0957274 | − | 0.0957274i | ||||
\(494\) | −10.3460 | + | 6.68097i | −0.465490 | + | 0.300591i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.937254 | + | 1.06275i | 0.0420839 | + | 0.0477187i | ||||
\(497\) | 12.2748 | 0.550602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5830 | − | 10.5830i | −0.473760 | − | 0.473760i | 0.429369 | − | 0.903129i | \(-0.358736\pi\) |
−0.903129 | + | 0.429369i | \(0.858736\pi\) | |||||||
\(500\) | −8.11905 | + | 3.06871i | −0.363095 | + | 0.137237i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.6458 | + | 5.52026i | 1.14463 | + | 0.246381i | ||||
\(503\) | − | 25.7424i | − | 1.14780i | −0.818926 | − | 0.573899i | \(-0.805430\pi\) | ||
0.818926 | − | 0.573899i | \(-0.194570\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 11.2915i | − | 0.502465i | ||||||
\(506\) | −2.77053 | + | 12.8712i | −0.123165 | + | 0.572195i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.2915 | − | 27.2288i | 0.545347 | − | 1.20808i | ||||
\(509\) | −27.2240 | − | 27.2240i | −1.20668 | − | 1.20668i | −0.972096 | − | 0.234585i | \(-0.924627\pi\) |
−0.234585 | − | 0.972096i | \(-0.575373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.5830 | −1.17596 | ||||||||
\(512\) | 20.3939 | − | 9.80250i | 0.901291 | − | 0.433213i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.4575 | − | 19.2915i | −0.549477 | − | 0.850912i | ||||
\(515\) | −2.52517 | − | 2.52517i | −0.111272 | − | 0.111272i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.41699 | + | 9.41699i | −0.414159 | + | 0.414159i | ||||
\(518\) | 7.12824 | − | 33.1160i | 0.313197 | − | 1.45503i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 35.1660 | − | 5.29150i | 1.54213 | − | 0.232048i | ||||
\(521\) | − | 18.7105i | − | 0.819720i | −0.912148 | − | 0.409860i | \(-0.865578\pi\) | ||
0.912148 | − | 0.409860i | \(-0.134422\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.06275 | + | 3.06275i | −0.133925 | + | 0.133925i | −0.770891 | − | 0.636967i | \(-0.780189\pi\) |
0.636967 | + | 0.770891i | \(0.280189\pi\) | |||||||
\(524\) | 4.45398 | − | 1.68345i | 0.194573 | − | 0.0735417i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.5830 | + | 12.0000i | −0.810258 | + | 0.523225i | ||||
\(527\) | −1.08709 | −0.0473543 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −38.1660 | −1.65939 | ||||||||
\(530\) | −30.7399 | + | 19.8504i | −1.33526 | + | 0.862244i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | − | 15.8745i | −0.260133 | − | 0.688247i | ||||
\(533\) | −17.0270 | + | 17.0270i | −0.737522 | + | 0.737522i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 45.1660i | − | 1.95270i | ||||||
\(536\) | 12.8712 | + | 9.50432i | 0.555951 | + | 0.410524i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.58301 | − | 16.6458i | 0.154474 | − | 0.717649i | ||||
\(539\) | 5.29570 | − | 5.29570i | 0.228102 | − | 0.228102i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.52026 | + | 8.52026i | 0.366315 | + | 0.366315i | 0.866131 | − | 0.499817i | \(-0.166599\pi\) |
−0.499817 | + | 0.866131i | \(0.666599\pi\) | |||||||
\(542\) | −8.93436 | − | 13.8356i | −0.383764 | − | 0.594290i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.70850 | + | 16.7085i | −0.201875 | + | 0.716371i | ||||
\(545\) | 6.43560 | 0.275671 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.937254 | − | 0.937254i | −0.0400741 | − | 0.0400741i | 0.686786 | − | 0.726860i | \(-0.259021\pi\) |
−0.726860 | + | 0.686786i | \(0.759021\pi\) | |||||||
\(548\) | −29.0565 | − | 13.1166i | −1.24123 | − | 0.560312i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.22876 | − | 10.3542i | 0.0950345 | − | 0.441507i | ||||
\(551\) | − | 2.27980i | − | 0.0971229i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.8745i | 0.675053i | ||||||||
\(554\) | −40.1216 | − | 8.63619i | −1.70460 | − | 0.366916i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.58301 | + | 17.4170i | 0.279182 | + | 0.738645i | ||||
\(557\) | 24.7516 | + | 24.7516i | 1.04876 | + | 1.04876i | 0.998749 | + | 0.0500103i | \(0.0159254\pi\) |
0.0500103 | + | 0.998749i | \(0.484075\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.8745 | 1.26356 | ||||||||
\(560\) | −3.06871 | + | 48.9068i | −0.129677 | + | 2.06669i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.2915 | + | 7.29150i | −0.476303 | + | 0.307573i | ||||
\(563\) | −16.4835 | − | 16.4835i | −0.694695 | − | 0.694695i | 0.268566 | − | 0.963261i | \(-0.413450\pi\) |
−0.963261 | + | 0.268566i | \(0.913450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −36.3338 | − | 7.82087i | −1.52722 | − | 0.328736i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.41699 | − | 9.41699i | −0.0594558 | − | 0.395128i | ||||
\(569\) | 11.9767i | 0.502088i | 0.967976 | + | 0.251044i | \(0.0807739\pi\) | ||||
−0.967976 | + | 0.251044i | \(0.919226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | − | 4.00000i | 0.167395 | − | 0.167395i | −0.618438 | − | 0.785833i | \(-0.712234\pi\) |
0.785833 | + | 0.618438i | \(0.212234\pi\) | |||||||
\(572\) | −3.66507 | + | 8.11905i | −0.153244 | + | 0.339475i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.0000 | − | 27.8745i | −0.751305 | − | 1.16346i | ||||
\(575\) | 49.2050 | 2.05199 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.0405 | 1.45876 | 0.729378 | − | 0.684111i | \(-0.239810\pi\) | ||||
0.729378 | + | 0.684111i | \(0.239810\pi\) | |||||||
\(578\) | 5.81752 | + | 9.00891i | 0.241977 | + | 0.374721i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.70850 | + | 6.00000i | −0.112464 | + | 0.249136i | ||||
\(581\) | −3.06871 | + | 3.06871i | −0.127312 | + | 0.127312i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9.16601i | − | 0.379617i | ||||||
\(584\) | 3.06871 | + | 20.3939i | 0.126984 | + | 0.843906i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.2288 | − | 6.29150i | −1.20743 | − | 0.259900i | ||||
\(587\) | 19.0086 | − | 19.0086i | 0.784570 | − | 0.784570i | −0.196028 | − | 0.980598i | \(-0.562804\pi\) |
0.980598 | + | 0.196028i | \(0.0628044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.583005 | − | 0.583005i | −0.0240223 | − | 0.0240223i | ||||
\(590\) | 44.1547 | − | 28.5129i | 1.81782 | − | 1.17386i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −26.2288 | − | 1.64575i | −1.07800 | − | 0.0676400i | ||||
\(593\) | 12.2748 | 0.504068 | 0.252034 | − | 0.967718i | \(-0.418901\pi\) | ||||
0.252034 | + | 0.967718i | \(0.418901\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.5830 | − | 26.5830i | −1.08980 | − | 1.08980i | ||||
\(596\) | 3.76135 | + | 9.95158i | 0.154071 | + | 0.407633i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −40.4575 | − | 8.70850i | −1.65443 | − | 0.356117i | ||||
\(599\) | 30.1964i | 1.23379i | 0.787045 | + | 0.616896i | \(0.211610\pi\) | ||||
−0.787045 | + | 0.616896i | \(0.788390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.29150i | 0.297427i | 0.988880 | + | 0.148713i | \(0.0475132\pi\) | ||||
−0.988880 | + | 0.148713i | \(0.952487\pi\) | |||||||
\(602\) | −8.66259 | + | 40.2443i | −0.353061 | + | 1.64023i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 28.5203 | + | 12.8745i | 1.16047 | + | 0.523856i | ||||
\(605\) | −22.7700 | − | 22.7700i | −0.925731 | − | 0.925731i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.1033 | −1.79010 | −0.895048 | − | 0.445970i | \(-0.852859\pi\) | ||||
−0.895048 | + | 0.445970i | \(0.852859\pi\) | |||||||
\(608\) | −11.4859 | + | 6.43560i | −0.465816 | + | 0.260998i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.9373 | + | 26.2288i | 0.685769 | + | 1.06197i | ||||
\(611\) | −29.6000 | − | 29.6000i | −1.19749 | − | 1.19749i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3542 | − | 21.3542i | 0.862490 | − | 0.862490i | −0.129137 | − | 0.991627i | \(-0.541221\pi\) |
0.991627 | + | 0.129137i | \(0.0412206\pi\) | |||||||
\(614\) | −8.41723 | + | 39.1044i | −0.339692 | + | 1.57812i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.87451 | − | 7.29150i | −0.397855 | − | 0.293783i | ||||
\(617\) | − | 25.7424i | − | 1.03635i | −0.855274 | − | 0.518175i | \(-0.826611\pi\) | ||
0.855274 | − | 0.518175i | \(-0.173389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1660 | − | 21.1660i | 0.850734 | − | 0.850734i | −0.139490 | − | 0.990224i | \(-0.544546\pi\) |
0.990224 | + | 0.139490i | \(0.0445462\pi\) | |||||||
\(620\) | 0.841723 | + | 2.22699i | 0.0338044 | + | 0.0894380i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.5830 | + | 12.0000i | −0.745111 | + | 0.481156i | ||||
\(623\) | 34.6504 | 1.38824 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.8745 | 0.674980 | ||||||||
\(626\) | −1.53436 | + | 0.990812i | −0.0613252 | + | 0.0396008i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.58301 | − | 1.35425i | 0.142977 | − | 0.0540404i | ||||
\(629\) | 14.2565 | − | 14.2565i | 0.568443 | − | 0.568443i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.2288i | 0.725675i | 0.931852 | + | 0.362838i | \(0.118192\pi\) | ||||
−0.931852 | + | 0.362838i | \(0.881808\pi\) | |||||||
\(632\) | 12.1786 | − | 1.83254i | 0.484438 | − | 0.0728943i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.00000 | − | 4.64575i | 0.0397151 | − | 0.184506i | ||||
\(635\) | 35.4921 | − | 35.4921i | 1.40846 | − | 1.40846i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.6458 | + | 16.6458i | 0.659529 | + | 0.659529i | ||||
\(638\) | −0.894538 | − | 1.38527i | −0.0354151 | − | 0.0548432i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 37.8745 | − | 3.29150i | 1.49712 | − | 0.130108i | ||||
\(641\) | 9.20614 | 0.363621 | 0.181810 | − | 0.983334i | \(-0.441804\pi\) | ||||
0.181810 | + | 0.983334i | \(0.441804\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.64575 | + | 1.64575i | 0.0649021 | + | 0.0649021i | 0.738813 | − | 0.673911i | \(-0.235387\pi\) |
−0.673911 | + | 0.738813i | \(0.735387\pi\) | |||||||
\(644\) | 23.4626 | − | 51.9756i | 0.924556 | − | 2.04812i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.12549 | − | 9.87451i | 0.0836264 | − | 0.388507i | ||||
\(647\) | 7.82087i | 0.307470i | 0.988112 | + | 0.153735i | \(0.0491302\pi\) | ||||
−0.988112 | + | 0.153735i | \(0.950870\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1660i | 0.516811i | ||||||||
\(650\) | 32.5461 | + | 7.00555i | 1.27656 | + | 0.274780i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.8118 | + | 6.35425i | −0.658399 | + | 0.248852i | ||||
\(653\) | 7.42642 | + | 7.42642i | 0.290618 | + | 0.290618i | 0.837324 | − | 0.546706i | \(-0.184119\pi\) |
−0.546706 | + | 0.837324i | \(0.684119\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | 0.312586 | ||||||||
\(656\) | −19.3068 | + | 17.0270i | −0.753804 | + | 0.664793i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 48.4575 | − | 31.2915i | 1.88907 | − | 1.21987i | ||||
\(659\) | −24.0590 | − | 24.0590i | −0.937204 | − | 0.937204i | 0.0609372 | − | 0.998142i | \(-0.480591\pi\) |
−0.998142 | + | 0.0609372i | \(0.980591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.2288 | + | 29.2288i | −1.13687 | + | 1.13687i | −0.147858 | + | 0.989009i | \(0.547238\pi\) |
−0.989009 | + | 0.147858i | \(0.952762\pi\) | |||||||
\(662\) | 15.6417 | + | 3.36689i | 0.607934 | + | 0.130858i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.70850 | + | 2.00000i | 0.105110 | + | 0.0776151i | ||||
\(665\) | − | 28.5129i | − | 1.10568i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.41699 | − | 5.41699i | 0.209747 | − | 0.209747i | ||||
\(668\) | 8.11905 | + | 3.66507i | 0.314135 | + | 0.141806i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.5830 | + | 22.5830i | 0.563391 | + | 0.872458i | ||||
\(671\) | −7.82087 | −0.301921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | −11.7313 | − | 18.1669i | −0.451873 | − | 0.699763i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.82288 | − | 0.822876i | −0.0701106 | − | 0.0316491i | ||||
\(677\) | 5.74297 | − | 5.74297i | 0.220720 | − | 0.220720i | −0.588081 | − | 0.808802i | \(-0.700117\pi\) |
0.808802 | + | 0.588081i | \(0.200117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.5830i | 1.48068i | ||||||||
\(680\) | −17.3252 | + | 23.4626i | −0.664391 | + | 0.899750i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.583005 | − | 0.125492i | −0.0223244 | − | 0.00480534i | ||||
\(683\) | −35.4921 | + | 35.4921i | −1.35807 | + | 1.35807i | −0.481769 | + | 0.876298i | \(0.660006\pi\) |
−0.876298 | + | 0.481769i | \(0.839994\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.8745 | − | 37.8745i | −1.44711 | − | 1.44711i | ||||
\(686\) | 3.06871 | − | 1.98162i | 0.117164 | − | 0.0756588i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31.8745 | + | 2.00000i | 1.21520 | + | 0.0762493i | ||||
\(689\) | 28.8111 | 1.09762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.64575 | + | 1.64575i | 0.0626073 | + | 0.0626073i | 0.737717 | − | 0.675110i | \(-0.235904\pi\) |
−0.675110 | + | 0.737717i | \(0.735904\pi\) | |||||||
\(692\) | −14.4056 | + | 5.44479i | −0.547617 | + | 0.206980i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.64575 | + | 0.354249i | 0.0624719 | + | 0.0134471i | ||||
\(695\) | 31.2835i | 1.18665i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 19.7490i | − | 0.748047i | ||||||
\(698\) | −9.77609 | + | 45.4173i | −0.370030 | + | 1.71907i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.8745 | + | 41.8118i | −0.713389 | + | 1.58034i | ||||
\(701\) | 16.6326 | + | 16.6326i | 0.628203 | + | 0.628203i | 0.947616 | − | 0.319413i | \(-0.103486\pi\) |
−0.319413 | + | 0.947616i | \(0.603486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2915 | 0.576730 | ||||||||
\(704\) | −4.45398 | + | 8.41723i | −0.167866 | + | 0.317236i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.8745 | + | 33.8745i | 0.823258 | + | 1.27488i | ||||
\(707\) | −8.66259 | − | 8.66259i | −0.325790 | − | 0.325790i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.2288 | + | 35.2288i | −1.32304 | + | 1.32304i | −0.411744 | + | 0.911299i | \(0.635080\pi\) |
−0.911299 | + | 0.411744i | \(0.864920\pi\) | |||||||
\(710\) | 3.36689 | − | 15.6417i | 0.126357 | − | 0.587024i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.00000 | − | 26.5830i | −0.149906 | − | 0.996240i | ||||
\(713\) | − | 2.77053i | − | 0.103757i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5830 | + | 10.5830i | −0.395782 | + | 0.395782i | ||||
\(716\) | −25.1461 | + | 9.50432i | −0.939752 | + | 0.355193i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.5830 | − | 14.5830i | 0.842790 | − | 0.544233i | ||||
\(719\) | 10.1007 | 0.376692 | 0.188346 | − | 0.982103i | \(-0.439687\pi\) | ||||
0.188346 | + | 0.982103i | \(0.439687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.87451 | −0.144294 | ||||||||
\(722\) | −16.1371 | + | 10.4206i | −0.600562 | + | 0.387814i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.64575 | + | 12.2915i | 0.172658 | + | 0.456810i | ||||
\(725\) | −4.35770 | + | 4.35770i | −0.161841 | + | 0.161841i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.3948i | 1.31272i | 0.754448 | + | 0.656360i | \(0.227905\pi\) | ||||
−0.754448 | + | 0.656360i | \(0.772095\pi\) | |||||||
\(728\) | 22.9191 | − | 31.0381i | 0.849437 | − | 1.15035i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.29150 | + | 33.8745i | −0.269871 | + | 1.25375i | ||||
\(731\) | −17.3252 | + | 17.3252i | −0.640795 | + | 0.640795i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.35425 | − | 7.35425i | −0.271635 | − | 0.271635i | 0.558123 | − | 0.829758i | \(-0.311522\pi\) |
−0.829758 | + | 0.558123i | \(0.811522\pi\) | |||||||
\(734\) | 9.82890 | + | 15.2209i | 0.362791 | + | 0.561813i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −42.5830 | − | 12.0000i | −1.56963 | − | 0.442326i | ||||
\(737\) | −6.73378 | −0.248042 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.1660 | + | 33.1660i | 1.22003 | + | 1.22003i | 0.967620 | + | 0.252411i | \(0.0812236\pi\) |
0.252411 | + | 0.967620i | \(0.418776\pi\) | |||||||
\(740\) | −40.2443 | − | 18.1669i | −1.47941 | − | 0.667829i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.35425 | + | 38.8118i | −0.306694 | + | 1.42482i | ||||
\(743\) | − | 14.5547i | − | 0.533958i | −0.963702 | − | 0.266979i | \(-0.913974\pi\) | ||
0.963702 | − | 0.266979i | \(-0.0860255\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.8745i | 0.654871i | ||||||||
\(746\) | 7.69819 | + | 1.65704i | 0.281851 | + | 0.0606685i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.58301 | − | 6.83399i | −0.0944440 | − | 0.249875i | ||||
\(749\) | −34.6504 | − | 34.6504i | −1.26610 | − | 1.26610i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.93725 | −0.107182 | −0.0535910 | − | 0.998563i | \(-0.517067\pi\) | ||||
−0.0535910 | + | 0.998563i | \(0.517067\pi\) | |||||||
\(752\) | −29.6000 | − | 33.5633i | −1.07940 | − | 1.22393i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.35425 | − | 2.81176i | 0.158572 | − | 0.102398i | ||||
\(755\) | 37.1755 | + | 37.1755i | 1.35296 | + | 1.35296i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.2288 | − | 19.2288i | 0.698881 | − | 0.698881i | −0.265288 | − | 0.964169i | \(-0.585467\pi\) |
0.964169 | + | 0.265288i | \(0.0854671\pi\) | |||||||
\(758\) | −26.6804 | − | 5.74297i | −0.969076 | − | 0.208594i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.8745 | + | 3.29150i | −0.793472 | + | 0.119395i | ||||
\(761\) | − | 6.43560i | − | 0.233290i | −0.993174 | − | 0.116645i | \(-0.962786\pi\) | ||
0.993174 | − | 0.116645i | \(-0.0372140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.93725 | − | 4.93725i | 0.178741 | − | 0.178741i | ||||
\(764\) | 9.20614 | − | 20.3939i | 0.333066 | − | 0.737825i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.58301 | − | 13.2915i | −0.310117 | − | 0.480242i | ||||
\(767\) | −41.3842 | −1.49430 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.70850 | 0.241915 | 0.120957 | − | 0.992658i | \(-0.461404\pi\) | ||||
0.120957 | + | 0.992658i | \(0.461404\pi\) | |||||||
\(770\) | −11.1878 | − | 17.3252i | −0.403179 | − | 0.624356i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.3542 | − | 36.2288i | 0.588602 | − | 1.30390i | ||||
\(773\) | −14.6509 | + | 14.6509i | −0.526957 | + | 0.526957i | −0.919664 | − | 0.392707i | \(-0.871539\pi\) |
0.392707 | + | 0.919664i | \(0.371539\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.22876i | 0.0800593i | ||||||||
\(776\) | 29.6000 | − | 4.45398i | 1.06258 | − | 0.159889i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.5203 | + | 3.12549i | 0.520577 | + | 0.112054i | ||||
\(779\) | 10.5914 | − | 10.5914i | 0.379476 | − | 0.379476i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.83399 | + | 2.83399i | 0.101408 | + | 0.101408i | ||||
\(782\) | 28.5129 | − | 18.4123i | 1.01962 | − | 0.658422i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.6458 | + | 18.8745i | 0.594491 | + | 0.674090i | ||||
\(785\) | 6.43560 | 0.229697 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.2288 | − | 20.2288i | −0.721077 | − | 0.721077i | 0.247747 | − | 0.968825i | \(-0.420310\pi\) |
−0.968825 | + | 0.247747i | \(0.920310\pi\) | |||||||
\(788\) | 8.81168 | + | 23.3135i | 0.313903 | + | 0.830510i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.2288 | + | 4.35425i | 0.719707 | + | 0.154917i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 24.5830i | − | 0.872968i | ||||||
\(794\) | 10.0743 | − | 46.8025i | 0.357522 | − | 1.66096i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.2288 | − | 6.87451i | −0.539769 | − | 0.243660i | ||||
\(797\) | 14.6509 | + | 14.6509i | 0.518962 | + | 0.518962i | 0.917257 | − | 0.398295i | \(-0.130398\pi\) |
−0.398295 | + | 0.917257i | \(0.630398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.3320 | 1.21458 | ||||||||
\(800\) | 34.2559 | + | 9.65341i | 1.21113 | + | 0.341299i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.06275 | − | 10.9373i | −0.249394 | − | 0.386208i | ||||
\(803\) | −6.13742 | − | 6.13742i | −0.216585 | − | 0.216585i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 67.7490 | − | 67.7490i | 2.38784 | − | 2.38784i | ||||
\(806\) | 0.394454 | − | 1.83254i | 0.0138941 | − | 0.0645483i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.64575 | + | 7.64575i | −0.198617 | + | 0.268977i | ||||
\(809\) | 44.4529i | 1.56288i | 0.623981 | + | 0.781440i | \(0.285514\pi\) | ||||
−0.623981 | + | 0.781440i | \(0.714486\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3542 | + | 10.3542i | −0.363587 | + | 0.363587i | −0.865132 | − | 0.501545i | \(-0.832765\pi\) |
0.501545 | + | 0.865132i | \(0.332765\pi\) | |||||||
\(812\) | 2.52517 | + | 6.68097i | 0.0886160 | + | 0.234456i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.29150 | − | 6.00000i | 0.325667 | − | 0.210300i | ||||
\(815\) | −30.1964 | −1.05773 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.5830 | −0.650137 | ||||||||
\(818\) | 20.3939 | − | 13.1694i | 0.713056 | − | 0.460457i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −40.4575 | + | 15.2915i | −1.41284 | + | 0.534002i | ||||
\(821\) | −30.8890 | + | 30.8890i | −1.07803 | + | 1.07803i | −0.0813488 | + | 0.996686i | \(0.525923\pi\) |
−0.996686 | + | 0.0813488i | \(0.974077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5.77124i | − | 0.201173i | −0.994928 | − | 0.100586i | \(-0.967928\pi\) | ||
0.994928 | − | 0.100586i | \(-0.0320719\pi\) | |||||||
\(824\) | 0.447269 | + | 2.97244i | 0.0155813 | + | 0.103550i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | − | 55.7490i | 0.417533 | − | 1.93976i | ||||
\(827\) | 7.82087 | − | 7.82087i | 0.271958 | − | 0.271958i | −0.557930 | − | 0.829888i | \(-0.688404\pi\) |
0.829888 | + | 0.557930i | \(0.188404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.35425 | + | 9.35425i | 0.324886 | + | 0.324886i | 0.850638 | − | 0.525752i | \(-0.176216\pi\) |
−0.525752 | + | 0.850638i | \(0.676216\pi\) | |||||||
\(830\) | 3.06871 | + | 4.75216i | 0.106517 | + | 0.164950i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26.4575 | − | 14.0000i | −0.917249 | − | 0.485363i | ||||
\(833\) | −19.3068 | −0.668941 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5830 | + | 10.5830i | 0.366240 | + | 0.366240i | ||||
\(836\) | 2.27980 | − | 5.05034i | 0.0788487 | − | 0.174670i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.52026 | − | 25.6458i | 0.190694 | − | 0.885918i | ||||
\(839\) | − | 40.1914i | − | 1.38756i | −0.720186 | − | 0.693781i | \(-0.755943\pi\) | ||
0.720186 | − | 0.693781i | \(-0.244057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.0405i | − | 0.966914i | ||||||
\(842\) | −32.5461 | − | 7.00555i | −1.12161 | − | 0.241427i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.4170 | + | 6.58301i | −0.599518 | + | 0.226596i | ||||
\(845\) | −2.37608 | − | 2.37608i | −0.0817396 | − | 0.0817396i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.9373 | −1.20046 | ||||||||
\(848\) | 30.7399 | + | 1.92881i | 1.05561 | + | 0.0662356i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −22.9373 | + | 14.8118i | −0.786741 | + | 0.508039i | ||||
\(851\) | 36.3338 | + | 36.3338i | 1.24551 | + | 1.24551i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.93725 | + | 3.93725i | −0.134809 | + | 0.134809i | −0.771291 | − | 0.636482i | \(-0.780389\pi\) |
0.636482 | + | 0.771291i | \(0.280389\pi\) | |||||||
\(854\) | 33.1160 | + | 7.12824i | 1.13321 | + | 0.243923i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.5830 | + | 30.5830i | −0.771871 | + | 1.04531i | ||||
\(857\) | 15.9399i | 0.544497i | 0.962227 | + | 0.272249i | \(0.0877673\pi\) | ||||
−0.962227 | + | 0.272249i | \(0.912233\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2288 | + | 32.2288i | −1.09963 | + | 1.09963i | −0.105178 | + | 0.994453i | \(0.533541\pi\) |
−0.994453 | + | 0.105178i | \(0.966459\pi\) | |||||||
\(860\) | 48.9068 | + | 22.0773i | 1.66771 | + | 0.752831i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.833990 | − | 1.29150i | −0.0284058 | − | 0.0439888i | ||||
\(863\) | 13.3619 | 0.454846 | 0.227423 | − | 0.973796i | \(-0.426970\pi\) | ||||
0.227423 | + | 0.973796i | \(0.426970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.8745 | −0.879760 | ||||||||
\(866\) | 3.06871 | + | 4.75216i | 0.104279 | + | 0.161485i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.35425 | + | 1.06275i | 0.0799084 | + | 0.0360720i | ||||
\(869\) | −3.66507 | + | 3.66507i | −0.124329 | + | 0.124329i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 21.1660i | − | 0.717183i | ||||||
\(872\) | −4.35770 | − | 3.21780i | −0.147570 | − | 0.108969i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.1660 | + | 5.41699i | 0.851253 | + | 0.183233i | ||||
\(875\) | −11.1878 | + | 11.1878i | −0.378215 | + | 0.378215i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.06275 | − | 6.06275i | −0.204724 | − | 0.204724i | 0.597296 | − | 0.802021i | \(-0.296242\pi\) |
−0.802021 | + | 0.597296i | \(0.796242\pi\) | |||||||
\(878\) | −44.5755 | + | 28.7847i | −1.50435 | + | 0.971437i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.0000 | + | 10.5830i | −0.404520 | + | 0.356753i | ||||
\(881\) | −40.7878 | −1.37418 | −0.687088 | − | 0.726574i | \(-0.741111\pi\) | ||||
−0.687088 | + | 0.726574i | \(0.741111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.3948 | + | 33.3948i | 1.12382 | + | 1.12382i | 0.991161 | + | 0.132662i | \(0.0423525\pi\) |
0.132662 | + | 0.991161i | \(0.457648\pi\) | |||||||
\(884\) | 21.4810 | − | 8.11905i | 0.722484 | − | 0.273073i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.3948 | + | 9.77124i | 1.52507 | + | 0.328271i | ||||
\(887\) | 19.0086i | 0.638247i | 0.947713 | + | 0.319124i | \(0.103389\pi\) | ||||
−0.947713 | + | 0.319124i | \(0.896611\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 54.4575i | − | 1.82645i | ||||||
\(890\) | 9.50432 | − | 44.1547i | 0.318585 | − | 1.48007i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.1660 | − | 35.8118i | 0.541278 | − | 1.19907i | ||||
\(893\) | 18.4123 | + | 18.4123i | 0.616143 | + | 0.616143i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.1660 | −1.50973 | ||||||||
\(896\) | 26.5313 | − | 31.5817i | 0.886349 | − | 1.05507i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.9373 | − | 44.8118i | −0.965649 | − | 1.49539i | ||||
\(899\) | 0.245364 | + | 0.245364i | 0.00818336 | + | 0.00818336i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.7085 | + | 16.7085i | −0.556641 | + | 0.556641i | ||||
\(902\) | 2.27980 | − | 10.5914i | 0.0759092 | − | 0.352655i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.0773i | 0.733876i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.1033 | + | 42.1033i | −1.39802 | + | 1.39802i | −0.592294 | + | 0.805722i | \(0.701778\pi\) |
−0.805722 | + | 0.592294i | \(0.798222\pi\) | |||||||
\(908\) | −48.0651 | + | 18.1669i | −1.59510 | + | 0.602890i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 54.4575 | − | 35.1660i | 1.80525 | − | 1.16574i | ||||
\(911\) | 45.8381 | 1.51869 | 0.759343 | − | 0.650691i | \(-0.225521\pi\) | ||||
0.759343 | + | 0.650691i | \(0.225521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.41699 | −0.0468957 | ||||||||
\(914\) | 31.5817 | − | 20.3939i | 1.04463 | − | 0.674570i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.06275 | + | 5.45751i | 0.0681550 | + | 0.180321i | ||||
\(917\) | 6.13742 | − | 6.13742i | 0.202676 | − | 0.202676i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.1033i | − | 0.531198i | −0.964084 | − | 0.265599i | \(-0.914430\pi\) | ||
0.964084 | − | 0.265599i | \(-0.0855697\pi\) | |||||||
\(920\) | −59.7964 | − | 44.1547i | −1.97143 | − | 1.45574i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.70850 | + | 17.2288i | −0.122133 | + | 0.567399i | ||||
\(923\) | −8.90796 | + | 8.90796i | −0.293209 | + | 0.293209i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.2288 | − | 29.2288i | −0.961036 | − | 0.961036i | ||||
\(926\) | −23.7344 | − | 36.7547i | −0.779960 | − | 1.20783i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.83399 | − | 2.70850i | 0.158683 | − | 0.0889108i | ||||
\(929\) | 19.3068 | 0.633436 | 0.316718 | − | 0.948520i | \(-0.397419\pi\) | ||||
0.316718 | + | 0.948520i | \(0.397419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.3542 | − | 10.3542i | −0.339347 | − | 0.339347i | ||||
\(932\) | 39.7007 | + | 17.9215i | 1.30044 | + | 0.587040i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.81176 | + | 22.3542i | −0.157446 | + | 0.731453i | ||||
\(935\) | − | 12.2748i | − | 0.401430i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 11.1660i | − | 0.364778i | −0.983226 | − | 0.182389i | \(-0.941617\pi\) | ||
0.983226 | − | 0.182389i | \(-0.0583830\pi\) | |||||||
\(938\) | 28.5129 | + | 6.13742i | 0.930981 | + | 0.200394i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26.5830 | − | 70.3320i | −0.867042 | − | 2.29398i | ||||
\(941\) | 25.8387 | + | 25.8387i | 0.842317 | + | 0.842317i | 0.989160 | − | 0.146843i | \(-0.0469111\pi\) |
−0.146843 | + | 0.989160i | \(0.546911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.3320 | 1.63904 | ||||||||
\(944\) | −44.1547 | − | 2.77053i | −1.43711 | − | 0.0901732i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.2915 | + | 7.29150i | −0.367118 | + | 0.237067i | ||||
\(947\) | 9.50432 | + | 9.50432i | 0.308849 | + | 0.308849i | 0.844463 | − | 0.535614i | \(-0.179920\pi\) |
−0.535614 | + | 0.844463i | \(0.679920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.2915 | − | 19.2915i | 0.626229 | − | 0.626229i | ||||
\(950\) | −20.2448 | − | 4.35770i | −0.656828 | − | 0.141383i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.70850 | + | 31.2915i | 0.152603 | + | 1.01416i | ||||
\(953\) | − | 24.8479i | − | 0.804902i | −0.915442 | − | 0.402451i | \(-0.868158\pi\) | ||
0.915442 | − | 0.402451i | \(-0.131842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.5830 | − | 26.5830i | 0.860206 | − | 0.860206i | ||||
\(956\) | 19.3068 | − | 42.7694i | 0.624427 | − | 1.38326i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.41699 | + | 14.5830i | 0.304249 | + | 0.471156i | ||||
\(959\) | −58.1130 | −1.87657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8745 | −0.995952 | ||||||||
\(962\) | 18.8595 | + | 29.2056i | 0.608056 | + | 0.941626i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.64575 | + | 16.9373i | −0.246253 | + | 0.545512i | ||||
\(965\) | 47.2234 | − | 47.2234i | 1.52018 | − | 1.52018i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3948i | 0.752325i | 0.926554 | + | 0.376162i | \(0.122757\pi\) | ||||
−0.926554 | + | 0.376162i | \(0.877243\pi\) | |||||||
\(968\) | 4.03312 | + | 26.8031i | 0.129629 | + | 0.861484i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 49.1660 | + | 10.5830i | 1.57863 | + | 0.339800i | ||||
\(971\) | −30.4418 | + | 30.4418i | −0.976923 | + | 0.976923i | −0.999740 | − | 0.0228172i | \(-0.992736\pi\) |
0.0228172 | + | 0.999740i | \(0.492736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.0000 | + | 24.0000i | 0.769405 | + | 0.769405i | ||||
\(974\) | −21.6565 | + | 13.9847i | −0.693918 | + | 0.448099i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.64575 | − | 26.2288i | 0.0526792 | − | 0.839562i | ||||
\(977\) | −43.8565 | −1.40309 | −0.701547 | − | 0.712623i | \(-0.747507\pi\) | ||||
−0.701547 | + | 0.712623i | \(0.747507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | + | 8.00000i | 0.255681 | + | 0.255681i | ||||
\(980\) | 14.9491 | + | 39.5516i | 0.477532 | + | 1.26343i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.2915 | − | 5.87451i | −0.870907 | − | 0.187463i | ||||
\(983\) | 6.73378i | 0.214774i | 0.994217 | + | 0.107387i | \(0.0342484\pi\) | ||||
−0.994217 | + | 0.107387i | \(0.965752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.8745i | 1.33423i | ||||||||
\(986\) | −0.894538 | + | 4.15580i | −0.0284879 | + | 0.132348i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.8745 | + | 7.16601i | 0.505035 | + | 0.227981i | ||||
\(989\) | −44.1547 | − | 44.1547i | −1.40404 | − | 1.40404i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.9373 | 0.601562 | 0.300781 | − | 0.953693i | \(-0.402753\pi\) | ||||
0.300781 | + | 0.953693i | \(0.402753\pi\) | |||||||
\(992\) | 0.543544 | − | 1.92881i | 0.0172575 | − | 0.0612398i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.41699 | − | 14.5830i | −0.298689 | − | 0.462545i | ||||
\(995\) | −19.8504 | − | 19.8504i | −0.629299 | − | 0.629299i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.520259 | + | 0.520259i | −0.0164768 | + | 0.0164768i | −0.715297 | − | 0.698820i | \(-0.753709\pi\) |
0.698820 | + | 0.715297i | \(0.253709\pi\) | |||||||
\(998\) | −4.45398 | + | 20.6921i | −0.140988 | + | 0.654996i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.2.k.c.109.2 | yes | 8 | |
3.2 | odd | 2 | inner | 144.2.k.c.109.3 | yes | 8 | |
4.3 | odd | 2 | 576.2.k.c.145.1 | 8 | |||
8.3 | odd | 2 | 1152.2.k.d.289.4 | 8 | |||
8.5 | even | 2 | 1152.2.k.e.289.4 | 8 | |||
12.11 | even | 2 | 576.2.k.c.145.4 | 8 | |||
16.3 | odd | 4 | 1152.2.k.d.865.4 | 8 | |||
16.5 | even | 4 | inner | 144.2.k.c.37.2 | ✓ | 8 | |
16.11 | odd | 4 | 576.2.k.c.433.1 | 8 | |||
16.13 | even | 4 | 1152.2.k.e.865.4 | 8 | |||
24.5 | odd | 2 | 1152.2.k.e.289.1 | 8 | |||
24.11 | even | 2 | 1152.2.k.d.289.1 | 8 | |||
32.5 | even | 8 | 9216.2.a.bq.1.1 | 8 | |||
32.11 | odd | 8 | 9216.2.a.bt.1.8 | 8 | |||
32.21 | even | 8 | 9216.2.a.bq.1.8 | 8 | |||
32.27 | odd | 8 | 9216.2.a.bt.1.1 | 8 | |||
48.5 | odd | 4 | inner | 144.2.k.c.37.3 | yes | 8 | |
48.11 | even | 4 | 576.2.k.c.433.4 | 8 | |||
48.29 | odd | 4 | 1152.2.k.e.865.1 | 8 | |||
48.35 | even | 4 | 1152.2.k.d.865.1 | 8 | |||
96.5 | odd | 8 | 9216.2.a.bq.1.7 | 8 | |||
96.11 | even | 8 | 9216.2.a.bt.1.2 | 8 | |||
96.53 | odd | 8 | 9216.2.a.bq.1.2 | 8 | |||
96.59 | even | 8 | 9216.2.a.bt.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.k.c.37.2 | ✓ | 8 | 16.5 | even | 4 | inner | |
144.2.k.c.37.3 | yes | 8 | 48.5 | odd | 4 | inner | |
144.2.k.c.109.2 | yes | 8 | 1.1 | even | 1 | trivial | |
144.2.k.c.109.3 | yes | 8 | 3.2 | odd | 2 | inner | |
576.2.k.c.145.1 | 8 | 4.3 | odd | 2 | |||
576.2.k.c.145.4 | 8 | 12.11 | even | 2 | |||
576.2.k.c.433.1 | 8 | 16.11 | odd | 4 | |||
576.2.k.c.433.4 | 8 | 48.11 | even | 4 | |||
1152.2.k.d.289.1 | 8 | 24.11 | even | 2 | |||
1152.2.k.d.289.4 | 8 | 8.3 | odd | 2 | |||
1152.2.k.d.865.1 | 8 | 48.35 | even | 4 | |||
1152.2.k.d.865.4 | 8 | 16.3 | odd | 4 | |||
1152.2.k.e.289.1 | 8 | 24.5 | odd | 2 | |||
1152.2.k.e.289.4 | 8 | 8.5 | even | 2 | |||
1152.2.k.e.865.1 | 8 | 48.29 | odd | 4 | |||
1152.2.k.e.865.4 | 8 | 16.13 | even | 4 | |||
9216.2.a.bq.1.1 | 8 | 32.5 | even | 8 | |||
9216.2.a.bq.1.2 | 8 | 96.53 | odd | 8 | |||
9216.2.a.bq.1.7 | 8 | 96.5 | odd | 8 | |||
9216.2.a.bq.1.8 | 8 | 32.21 | even | 8 | |||
9216.2.a.bt.1.1 | 8 | 32.27 | odd | 8 | |||
9216.2.a.bt.1.2 | 8 | 96.11 | even | 8 | |||
9216.2.a.bt.1.7 | 8 | 96.59 | even | 8 | |||
9216.2.a.bt.1.8 | 8 | 32.11 | odd | 8 |